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<div class="title">HessenbergDecomposition.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2008-2009 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2010 Jitse Niesen &lt;jitse@maths.leeds.ac.uk&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_HESSENBERGDECOMPOSITION_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_HESSENBERGDECOMPOSITION_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;  </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt; <span class="keyword">struct </span>HessenbergDecompositionMatrixHReturnType;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="keyword">struct </span>traits&lt;HessenbergDecompositionMatrixHReturnType&lt;MatrixType&gt; &gt;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;{</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  <span class="keyword">typedef</span> MatrixType ReturnType;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;};</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160; </div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;}</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html">   59</a></span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_&gt; <span class="keyword">class </span><a class="code" href="classEigen_1_1HessenbergDecomposition.html">HessenbergDecomposition</a></div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;{</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#ae7caa77e42d01241ee2acb653e878431">   64</a></span>&#160;    <span class="keyword">typedef</span> MatrixType_ <a class="code" href="classEigen_1_1HessenbergDecomposition.html#ae7caa77e42d01241ee2acb653e878431">MatrixType</a>;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;      Size = MatrixType::RowsAtCompileTime,</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;      SizeMinusOne = Size == <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> : Size - 1,</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;      Options = MatrixType::Options,</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;      MaxSize = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;      MaxSizeMinusOne = MaxSize == <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> : MaxSize - 1</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;    };</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160; </div>
<div class="line"><a name="l00075"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a31c9b1902c14a85109da3fd9b7b1f221">   75</a></span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a31c9b1902c14a85109da3fd9b7b1f221">Scalar</a>;</div>
<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a94e001b3a7c99b1813cfeba43e947eef">   76</a></span>&#160;    <span class="keyword">typedef</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a94e001b3a7c99b1813cfeba43e947eef">Index</a>; </div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160; </div>
<div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a02f99fc02c6d591efa640febabb5c085">   84</a></span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;Scalar, SizeMinusOne, 1, Options &amp; ~RowMajor, MaxSizeMinusOne, 1&gt;</a> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a02f99fc02c6d591efa640febabb5c085">CoeffVectorType</a>;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a92df4f5e754ee6f69fcfa825aad49633">   87</a></span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequence&lt;MatrixType,internal::remove_all_t&lt;typename CoeffVectorType::ConjugateReturnType&gt;</a>&gt; <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a92df4f5e754ee6f69fcfa825aad49633">HouseholderSequenceType</a>;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    </div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    <span class="keyword">typedef</span> internal::HessenbergDecompositionMatrixHReturnType&lt;MatrixType&gt; MatrixHReturnType;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160; </div>
<div class="line"><a name="l00102"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a0dad58827e37748391d463674d80bcf4">  102</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a0dad58827e37748391d463674d80bcf4">HessenbergDecomposition</a>(<a class="code" href="classEigen_1_1HessenbergDecomposition.html#a94e001b3a7c99b1813cfeba43e947eef">Index</a> size = Size==<a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? 2 : Size)</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;      : m_matrix(size,size),</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        m_temp(size),</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        m_isInitialized(false)</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    {</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;      <span class="keywordflow">if</span>(size&gt;1)</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;        m_hCoeffs.<a class="code" href="classEigen_1_1PlainObjectBase.html#a9fd0703bd7bfe89d6dc80e2ce87c312a">resize</a>(size-1);</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    }</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; </div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00121"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a4e2aeb88b7d1d9f580f33d3c7735c9e7">  121</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a4e2aeb88b7d1d9f580f33d3c7735c9e7">HessenbergDecomposition</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;      : m_matrix(matrix.derived()),</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;        m_temp(matrix.rows()),</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;        m_isInitialized(false)</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;    {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;      <span class="keywordflow">if</span>(matrix.<a class="code" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>()&lt;2)</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;      {</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;        m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;        <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;      }</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;      m_hCoeffs.<a class="code" href="classEigen_1_1PlainObjectBase.html#a9fd0703bd7bfe89d6dc80e2ce87c312a">resize</a>(matrix.<a class="code" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>()-1,1);</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;      _compute(m_matrix, m_hCoeffs, m_temp);</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;      m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;    }</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00154"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a41716f3e086ba668cd062e28dcf3bd68">  154</a></span>&#160;    <a class="code" href="classEigen_1_1HessenbergDecomposition.html">HessenbergDecomposition</a>&amp; <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a41716f3e086ba668cd062e28dcf3bd68">compute</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;    {</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;      m_matrix = matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>();</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;      <span class="keywordflow">if</span>(matrix.<a class="code" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>()&lt;2)</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;      {</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;        m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;        <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;      }</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;      m_hCoeffs.<a class="code" href="classEigen_1_1PlainObjectBase.html#a9fd0703bd7bfe89d6dc80e2ce87c312a">resize</a>(matrix.<a class="code" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>()-1,1);</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;      _compute(m_matrix, m_hCoeffs, m_temp);</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;      m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;      <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    }</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160; </div>
<div class="line"><a name="l00181"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a0380ce1c92729c93e60e187ceb02636f">  181</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1Matrix.html">CoeffVectorType</a>&amp; <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a0380ce1c92729c93e60e187ceb02636f">householderCoefficients</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;HessenbergDecomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;      <span class="keywordflow">return</span> m_hCoeffs;</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    }</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160; </div>
<div class="line"><a name="l00216"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a897bed38fdb772f68fcbc80389ccd593">  216</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#ae7caa77e42d01241ee2acb653e878431">MatrixType</a>&amp; <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a897bed38fdb772f68fcbc80389ccd593">packedMatrix</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;HessenbergDecomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;      <span class="keywordflow">return</span> m_matrix;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;    }</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160; </div>
<div class="line"><a name="l00236"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a89702bceeb4b3d4ebedeb62d4f3e224b">  236</a></span>&#160;    <a class="code" href="classEigen_1_1HouseholderSequence.html">HouseholderSequenceType</a> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a89702bceeb4b3d4ebedeb62d4f3e224b">matrixQ</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;HessenbergDecomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;      <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a92df4f5e754ee6f69fcfa825aad49633">HouseholderSequenceType</a>(m_matrix, m_hCoeffs.conjugate())</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;             .setLength(m_matrix.rows() - 1)</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;             .setShift(1);</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    }</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160; </div>
<div class="line"><a name="l00264"></a><span class="lineno"><a class="line" href="classEigen_1_1HessenbergDecomposition.html#a860542861de9cfec2543423c7313d7a2">  264</a></span>&#160;    MatrixHReturnType <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a860542861de9cfec2543423c7313d7a2">matrixH</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;HessenbergDecomposition is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;      <span class="keywordflow">return</span> MatrixHReturnType(*<span class="keyword">this</span>);</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;    }</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160; </div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160; </div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix</a>&lt;<a class="code" href="classEigen_1_1HessenbergDecomposition.html#a31c9b1902c14a85109da3fd9b7b1f221">Scalar</a>, 1, Size, int(Options) | int(<a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>), 1, MaxSize&gt; VectorType;</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::Real</a> RealScalar;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    <span class="keyword">static</span> <span class="keywordtype">void</span> _compute(<a class="code" href="classEigen_1_1HessenbergDecomposition.html#ae7caa77e42d01241ee2acb653e878431">MatrixType</a>&amp; matA, <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a02f99fc02c6d591efa640febabb5c085">CoeffVectorType</a>&amp; hCoeffs, VectorType&amp; temp);</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160; </div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;    <a class="code" href="classEigen_1_1HessenbergDecomposition.html#ae7caa77e42d01241ee2acb653e878431">MatrixType</a> m_matrix;</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;    <a class="code" href="classEigen_1_1HessenbergDecomposition.html#a02f99fc02c6d591efa640febabb5c085">CoeffVectorType</a> m_hCoeffs;</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    VectorType m_temp;</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;    <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;};</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160; </div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;<span class="keywordtype">void</span> HessenbergDecomposition&lt;MatrixType&gt;::_compute(MatrixType&amp; matA, CoeffVectorType&amp; hCoeffs, VectorType&amp; temp)</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;{</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  eigen_assert(matA.rows()==matA.cols());</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  Index n = matA.rows();</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  temp.resize(n);</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;  <span class="keywordflow">for</span> (Index i = 0; i&lt;n-1; ++i)</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;  {</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    <span class="comment">// let&#39;s consider the vector v = i-th column starting at position i+1</span></div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;    Index remainingSize = n-i-1;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;    RealScalar beta;</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    Scalar h;</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    matA.col(i).tail(remainingSize).makeHouseholderInPlace(h, beta);</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    matA.col(i).coeffRef(i+1) = beta;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    hCoeffs.coeffRef(i) = h;</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160; </div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    <span class="comment">// Apply similarity transformation to remaining columns,</span></div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;    <span class="comment">// i.e., compute A = H A H&#39;</span></div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160; </div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;    <span class="comment">// A = H A</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;    matA.bottomRightCorner(remainingSize, remainingSize)</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;        .applyHouseholderOnTheLeft(matA.col(i).tail(remainingSize-1), h, &amp;temp.coeffRef(0));</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160; </div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    <span class="comment">// A = A H&#39;</span></div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    matA.rightCols(remainingSize)</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;        .applyHouseholderOnTheRight(matA.col(i).tail(remainingSize-1), numext::conj(h), &amp;temp.coeffRef(0));</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  }</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;}</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160; </div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160; </div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt; <span class="keyword">struct </span>HessenbergDecompositionMatrixHReturnType</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;: <span class="keyword">public</span> ReturnByValue&lt;HessenbergDecompositionMatrixHReturnType&lt;MatrixType&gt; &gt;</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;{</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    HessenbergDecompositionMatrixHReturnType(<span class="keyword">const</span> HessenbergDecomposition&lt;MatrixType&gt;&amp; hess) : m_hess(hess) { }</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160; </div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> ResultType&gt;</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">void</span> evalTo(ResultType&amp; result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;      result = m_hess.packedMatrix();</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = result.rows();</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;      <span class="keywordflow">if</span> (n&gt;2)</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;        result.bottomLeftCorner(n-2, n-2).template triangularView&lt;Lower&gt;().setZero();</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;    }</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160; </div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_hess.packedMatrix().rows(); }</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_hess.packedMatrix().cols(); }</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160; </div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;    <span class="keyword">const</span> HessenbergDecomposition&lt;MatrixType&gt;&amp; m_hess;</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;};</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160; </div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160; </div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160; </div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_HESSENBERGDECOMPOSITION_H</span></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html">Eigen::HessenbergDecomposition</a></div><div class="ttdoc">Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:60</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a02f99fc02c6d591efa640febabb5c085"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a02f99fc02c6d591efa640febabb5c085">Eigen::HessenbergDecomposition::CoeffVectorType</a></div><div class="ttdeci">Matrix&lt; Scalar, SizeMinusOne, 1, Options &amp;~RowMajor, MaxSizeMinusOne, 1 &gt; CoeffVectorType</div><div class="ttdoc">Type for vector of Householder coefficients.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:84</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a0380ce1c92729c93e60e187ceb02636f"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a0380ce1c92729c93e60e187ceb02636f">Eigen::HessenbergDecomposition::householderCoefficients</a></div><div class="ttdeci">const CoeffVectorType &amp; householderCoefficients() const</div><div class="ttdoc">Returns the Householder coefficients.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:181</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a0dad58827e37748391d463674d80bcf4"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a0dad58827e37748391d463674d80bcf4">Eigen::HessenbergDecomposition::HessenbergDecomposition</a></div><div class="ttdeci">HessenbergDecomposition(Index size=Size==Dynamic ? 2 :Size)</div><div class="ttdoc">Default constructor; the decomposition will be computed later.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:102</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a31c9b1902c14a85109da3fd9b7b1f221"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a31c9b1902c14a85109da3fd9b7b1f221">Eigen::HessenbergDecomposition::Scalar</a></div><div class="ttdeci">MatrixType::Scalar Scalar</div><div class="ttdoc">Scalar type for matrices of type MatrixType.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:75</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a41716f3e086ba668cd062e28dcf3bd68"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a41716f3e086ba668cd062e28dcf3bd68">Eigen::HessenbergDecomposition::compute</a></div><div class="ttdeci">HessenbergDecomposition &amp; compute(const EigenBase&lt; InputType &gt; &amp;matrix)</div><div class="ttdoc">Computes Hessenberg decomposition of given matrix.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:154</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a4e2aeb88b7d1d9f580f33d3c7735c9e7"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a4e2aeb88b7d1d9f580f33d3c7735c9e7">Eigen::HessenbergDecomposition::HessenbergDecomposition</a></div><div class="ttdeci">HessenbergDecomposition(const EigenBase&lt; InputType &gt; &amp;matrix)</div><div class="ttdoc">Constructor; computes Hessenberg decomposition of given matrix.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:121</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a860542861de9cfec2543423c7313d7a2"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a860542861de9cfec2543423c7313d7a2">Eigen::HessenbergDecomposition::matrixH</a></div><div class="ttdeci">MatrixHReturnType matrixH() const</div><div class="ttdoc">Constructs the Hessenberg matrix H in the decomposition.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:264</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a89702bceeb4b3d4ebedeb62d4f3e224b"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a89702bceeb4b3d4ebedeb62d4f3e224b">Eigen::HessenbergDecomposition::matrixQ</a></div><div class="ttdeci">HouseholderSequenceType matrixQ() const</div><div class="ttdoc">Reconstructs the orthogonal matrix Q in the decomposition.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:236</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a897bed38fdb772f68fcbc80389ccd593"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a897bed38fdb772f68fcbc80389ccd593">Eigen::HessenbergDecomposition::packedMatrix</a></div><div class="ttdeci">const MatrixType &amp; packedMatrix() const</div><div class="ttdoc">Returns the internal representation of the decomposition.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:216</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a92df4f5e754ee6f69fcfa825aad49633"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a92df4f5e754ee6f69fcfa825aad49633">Eigen::HessenbergDecomposition::HouseholderSequenceType</a></div><div class="ttdeci">HouseholderSequence&lt; MatrixType, internal::remove_all_t&lt; typename CoeffVectorType::ConjugateReturnType &gt; &gt; HouseholderSequenceType</div><div class="ttdoc">Return type of matrixQ()</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:87</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_a94e001b3a7c99b1813cfeba43e947eef"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#a94e001b3a7c99b1813cfeba43e947eef">Eigen::HessenbergDecomposition::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:76</div></div>
<div class="ttc" id="aclassEigen_1_1HessenbergDecomposition_html_ae7caa77e42d01241ee2acb653e878431"><div class="ttname"><a href="classEigen_1_1HessenbergDecomposition.html#ae7caa77e42d01241ee2acb653e878431">Eigen::HessenbergDecomposition::MatrixType</a></div><div class="ttdeci">MatrixType_ MatrixType</div><div class="ttdoc">Synonym for the template parameter MatrixType_.</div><div class="ttdef"><b>Definition:</b> HessenbergDecomposition.h:64</div></div>
<div class="ttc" id="aclassEigen_1_1HouseholderSequence_html"><div class="ttname"><a href="classEigen_1_1HouseholderSequence.html">Eigen::HouseholderSequence</a></div><div class="ttdoc">Sequence of Householder reflections acting on subspaces with decreasing size.</div><div class="ttdef"><b>Definition:</b> HouseholderSequence.h:123</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix&lt; Scalar, SizeMinusOne, 1, Options &amp;~RowMajor, MaxSizeMinusOne, 1 &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1PlainObjectBase_html_a9fd0703bd7bfe89d6dc80e2ce87c312a"><div class="ttname"><a href="classEigen_1_1PlainObjectBase.html#a9fd0703bd7bfe89d6dc80e2ce87c312a">Eigen::PlainObjectBase::resize</a></div><div class="ttdeci">void resize(Index rows, Index cols)</div><div class="ttdef"><b>Definition:</b> PlainObjectBase.h:283</div></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">Eigen::RowMajor</a></div><div class="ttdeci">@ RowMajor</div><div class="ttdef"><b>Definition:</b> Constants.h:323</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:24</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition:</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_ac22eb0695d00edd7d4a3b2d0a98b81c2"><div class="ttname"><a href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">Eigen::EigenBase::rows</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:62</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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